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Djeca rane i predškolske dobi se u svojoj okolini svakodnevno susreću s osnovama geometrijskih pojmova. S obzirom da na razvoj geometrijskog mišljenja ne utječe krononološka dob cilj ovog diplomskog rada je ispitati na kojoj se razini geometrijskog mišljenja prema van Hiele-ovoj teoriji nalaze djeca rane i predškolske dobi. Na početku rada opisan je razvoj van Hiele-ove teorije o razvoju mišljenja. Zatim su navedene razine geometrijskog mišljenja, a to su: razina prepoznavanja, razina analize, razine neformalne dedukcije, razina formalne dedukcije te razina strogosti. Osim toga, navedeni su objekti i proizvodi geometrijskog mišljenja za svaku razinu. Svaka razina učenja je potom opisana te su iznesene njihove karakteristike. TakoĎer su opisane osnovne karakteristike van Hiele-ovog modela razvoja mišljenja, kao i faze učenja koje mogu biti korisne pri planiranju i organizaciji nastave, ali i predškolskih aktivnosti. Za potrebe ovog diplomskog rada provedeno je istraţivanje u kojem su sudjelovala djeca rane i predškolske dobi. PonuĎena su im dva testa kojima se htjelo utvrditi na koji način percipiraju geometrijske oblike u svojoj svakodnevici. Na kraju rada navedeni su primjeri za poticanje razvoja geometrijskog mišljenja kod djece ranog i predškolskog uzrasta. Children of early and preschool age encounter the basics of geometric concepts in their environment every day. Given that the development of geometric thinking is not affected by chronological age, the goal of this thesis is to examine at which level of geometric thinking according to van Hiele's theory children of early and preschool age are at. At the beginning of the paper, the development of van Hiele's theory on the development of thinking is described. Then the levels of geometric thinking are listed, namely: the level of recognition, the level of analysis, the levels of informal deduction, the level of formal deduction and the level of rigor. In addition, objects and products of geometric thinking are listed for each level. Each level of learning is then described and their characteristics are presented. The basic characteristics of van Hiele's model of thinking development are also described, as well as the stages of learning that can be useful in planning and organizing classes, as well as preschool activities. For the purposes of this thesis, a research was conducted in which children of early and preschool age participated. They were offered two tests to determine how they perceive geometric shapes in their everyday life. At the end of the paper, examples are given for encouraging the development of geometric thinking in children of early and preschool age.

Istražujući osnovne značajke geometrije u odabranim poljima djelovanja, kroz ovaj rad proteže se osnovna ideja principa geometrije kao poticaj za stvaranje vlastite modne kolekcije. Kroz istraživački dio rada, osvrćem se na samu povijest i početke poznavanja i primjenjivanja ove matematičke discipline. Inspiraciju za stvaranje modne kolekcije dalje pronalazim istražujući geometriju u umjetnosti i modi kroz povijest te ističem nekolicinu odabranih umjetničkih razdoblja, umjetnika i dizajnera koji su stvarali potaknuti upravo osnovnim načelima geometrije. U konačnici, završavam ovaj rad modnom kolekcijom kroz praktični dio prikaza petnaest skica modela., While analyzing the basic features of geometry through selected fields of activity, this project extends the idea of base geometry principle as an incentive for creating a fashion collection. During the research part of the paper, I look back at the very beginnings and history of knowledge and application of this mathematical discipline. Furthermore, my inspiration for the creation of a fashion collection comes from understanding and implementing geometry in art andfashion throughout history and highlighting a few selected artistic periods, artists and designers, whose creations were inspired by the basic principles of geometry. Ultimately, I conclude this paper with a fashion collection, utilizing fifteen sketch models of my own making as a practical part of the presentation.

U radu je prikazana nova metoda određivanja optimalnog oblika gornje elektrode u RRAM ćelijama s promjenom valencije. Konstruiran je stohastički model rasta vodljivog vlakna (CF), koji se fokusirao samo na fazu formiranja. Napon prekida simulacije korišten je kao procjena za određivanje varijabilnosti vodljivosti u stanju niskog otpora. Optimizacija oblika gornje elektrode provedena je pomoću genetskog algoritma. Primijenjena je inovativna strategija mutacije, koja uzima u obzir povijest populacije, uz strategiju odabira putem eksponencijalne rang selekcije. Optimalni oblik elektrode, do broja epoha genetskog algoritma, prikazan je u odjeljku Rezultati. The paper presents a novel method of determining optimal top electrode shape in valence change RRAM cells. A model of stochastic conductive filament (CF) growth was constructed, which focused only on the formation phase. The cutoff voltage was used as a proxy for determining the conductance variability in the low resistance state. Optimization of the top electrode shape was performed using a genetic algorithm. An innovative mutation strategy, which takes into account the history of the population, was employed, alongside an exponential rank selection strategy. The optimal electrode shape, up to the number of genetic algorithm epochs, is presented in the Results section.

U ovom radu zanimat će nas područje incidencijskih geometrija koje se sastoje od nepraznog skupa točaka i pravaca te je njihova veza opisana relacijom incidencije. Proučavat ćemo neke najpoznatije familije tih geometrija te istražiti i neka njihova svojstva., In this paper, we will be interested in the field of incidence geometries, which consist of a non-empty set of points and a possibily empty set of lines, and their connection is described by the incidence relation. We will study some of the most famous families of these geometries and show some of their properties.

Kroz ovaj rad proučava se život i opus jednog od najvećih modnih dizajnera 20. stoljeća i njegova načela stvaranja odjevnih predmeta. Kroz analizu i istraživanje proučavaju se njegova načela izrade odjeće, geometričnosti, jednostavnosti i sklada u modi. Iz istraživanja će proizaći vlastita kolekcija inspirirana tim načelima i stvaranje vlastite modne kreacije. Krajnji cilj ovog istraživanja je na vlastitoj kolekciji prikazati primjenu načela Cristobala Balenciage., This paper examines the life and work of one of the greatest fashion designer of the 20th century and his principles of creating garments. Through the analysis and research of his principles of geometry, simplicity and harmony in fashion are studied. From the research comes a collection inspired by these principles and new fashion creations are made. The final goal of this research is to present the application of the Cristobal Balenciaga principles into a new collection.